>: A story such as "The 4-D Doodler," that speculates about>: a fourth spacial dimension, one dimension beyond our>: known world of three dimensions, seemed promising to me,>: the dilettante, at first. Perhaps 4-dimensional space>: uses an exotic infinity. Alas, as Wolfram notes, it's>: the same old infinity. An infinity that's independent>: of spacial dimensions.

> It's c, or aleph-1 maybe, or whatnot.

It's c, or 2^\omega.

> It is not the infinity of natural numbers; it's bigger. > So there's at least two infinities, not the "same old> infinity". Similarly, the cardinality of the set of paths> in n>=2 d space (if I'm remembering a close enough> description) is bigger still.